Valence-to-conduction band transitions

The photoconductivity and absorption spectra of the multilayer polydiacetylene are shown in Fig. 22 [150]. The continuous and dotted line relate to the blue and red polymer forms respectively. Interpretation is given in terms of a valence to conduction band transition which is buried under the vibronic sidebands of the dominant exciton transition. The associated absorption coefficient follows a law which indicates either an indirect transition or a direct transition between non-parabolic bands. The gap energies are 2.5 eV and 2.6 eV for the two different forms. The transition is three dimensional indicating finite valence and conduction band dispersion in the direction perpendicular to the polymer chain. 

However, absorption and photoconduction spectra do not reveal any correspondence , which suggests that the dominant optical transition is photoelectrically inactive and cannot be a valence-to-conduction band transition. Further analysis of the data in terms of a model considering a valence-to-conduction band transition, which is buried under the vibronic side bands of the dominant excitonic transition, yielded a gap energy = 2.5 0.1 eV for the blue layer (absorption peak at 1.94 eV) and = 2.6 0.1 eV for the red layer (absorption peak at 2.33 eV), in good agreement to other polydlacetylenes... 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

The excitation mechanism consists of electron transitions from the valence to conduction band of the lattice followed by... 

Donor-acceptor absorption can also be observed in semiconductors, but this process is weak because of the small overlap of the wavefunctions (like an n -> n transition). Donor-acceptor absorption is best monitored through the emission, that is by excitation spectra. In the normal situation, the donor-acceptor absorption can be observed but the valence band-to-donor and the acceptor-to-conduction band transitions can also be seen, as they also contribute to the luminescence. All three of these transitions are weak but of similar strengths [6]. In undoped AgCl and AgBr, only a very weak excitation spectrum is seen, which consists of a relatively sharp line near the band edge. In Cd2 + doped AgBr both the sharper line, whose onset is about... 

Since bulk CdS shows free-exciton emission at low temperatures [34], it is interesting to compare these results on CdS with the discussion in Sect. 3.3.9b on the transition from semiconductors to insulators. There it was shown that narrow-line free-exciton emission transforms into broad-band localized emission, if the amount of delocalization of the excited state decreases. Since the valence band to conduction band transition of CdS is in principle a - Cd " " charge-transfer transition, this would bring the discussion on CdS in line with results from a different origin (see Sect. 3.3.9b). By all means the case of Cd32S 4(SC(,Hs)35.DMF4 is a nice example of luminescence research on a well-defined cluster showing the quantum-size effect. 

Thermal energy at T > 0 K can excite electrons from the valence to conduction band. The excited conduction band electron leaves behind an empty state in the valence band often termed a hole. When such a transition occurs, both bands are now partially filled and conduction can take place. It is important to note that charge carrier motion in a semiconductor is strongly influenced by scattering events at atomic centers and by the electric fields that exist between those points. To simplify the mathematical description of these phenomena, the masses of the electrons and holes are often described within the effective mass approximation where the free electron mass, is replaced with the effective mass (w for electrons or m for holes). 

Quantum effects are observed in the Raman spectra of SWCNTs through the resonant Raman enhancement process, which is seen experimentally by measuring the Raman spectra at a number of laser excitation energies. Resonant enhancement in the Raman scattering intensity from CNTs occurs when the laser excitation energy corresponds to an electronic transition between the sharp features (i.e., (E - ,)" type singularities at energy ,) in the ID electronic DOS of the valence and conduction bands of the carbon CNT. 

Optical band gap energies (Eg) for WOx-ZrOa samples calcined at 1073 K were obtained from UV-vis spectra using procedures based on direct and indirect transitions between valence and conduction bands [26]. Direct band gap energies (Egdecreased monotonically from 4.15 to 3.75 eV as the W loading increased from 3.05 to 15.0 W-atomsnm (Table 2). 

The corresponding quantum mechanical expression of s op in Equation (4.19) is similar except for the quantity Nj, which is replaced by Nfj. However, the physical meaning of some terms are quite different coj represents the frequency corresponding to a transition between two electronic states of the atom separated by an energy Ticoj, and fj is a dimensionless quantity (called the oscillator strength and formally defined in the next chapter, in Section 5.3) related to the quantum probability for this transition, satisfying Jfj fj = l- At this point, it is important to mention that the multiple resonant frequencies coj could be related to multiple valence band to conduction band singularities (transitions), or to transitions due to optical centers. This model does not differentiate between these possible processes it only relates the multiple resonances to different resonance frequencies. 

The absorption spectrum involving the valence band to first empty (conduction) band transitions is usually called the fundamental absorption spectrum. For many crystals, this spectrum lies within the optical range. 

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